Title:
"Observables" in causal set cosmology

Abstract: The ``generic'' family of classical sequential growth dynamics for causal
sets provides cosmological models of causal sets which are a testing ground for
ideas about the, as yet unknown, quantum theory. In particular we can
investigate how general covariance manifests itself and address the problem of
identifying and interpreting covariant ``observables'' in quantum gravity. The
problem becomes, in this setting, that of identifying measurable covariant
collections of causal sets, to each of which corresponds the question: ``Does
the causal set that occurs belong to this collection?'' It has for answer the
probability measure of the collection. Answerable covariant questions, then,
correspond to measurable collections of causal sets which are independent of
the labelings of the causal sets. However, what the transition probabilities of
the classical sequential growth dynamics provide directly is a measure on the
space of {\it labeled} causal sets and the physical interpretation of the
covariant measurable collections is consequently obscured. We show that there
is a physically meaningful characterisation of the class of measurable
covariant sets as unions and differences of ``stem sets''.